涓�冩�诲涔?/p>
12
浜屾鍑芥暟
1
銆佸畾涔夛細
涓�鑸殑锛屽舰濡?/p>
y
=
ax
2
+
bx
+
c
(
a
銆?/p>
b
銆?/p>
c
鏄父鏁帮紝
a
鈮?/p>
0)
鐨勫嚱鏁板彨鍋氫簩娆″嚱鏁般�傚叾涓?/p>
x
鏄嚜鍙橀噺锛?/p>
a
銆?/p>
b
銆?/p>
c
鍒嗗埆鏄嚱鏁拌В鏋愬紡鐨勪簩娆￠」绯绘暟銆佷竴娆￠」绯绘暟銆佸父鏁伴」銆?/p>
2
銆?/p>
浜屾鍑芥暟鐨勫浘璞℃槸涓�鏉℃姏鐗╃嚎銆傚綋
a
锛?/p>
0
鏃讹紝鎶涚墿绾垮紑鍙ｅ悜涓婏紱褰?/p>
a
锛?/p>
0
鏃讹紝鎶涚墿绾?/p>
寮�鍙ｅ悜涓嬨�?/p>
|
a
|
瓒婂ぇ锛屾姏鐗╃嚎鐨勫紑鍙ｈ秺灏忥紱
|
a
|
瓒婂皬锛屾姏鐗╃嚎鐨勫紑鍙ｈ秺澶с�?/p>
y
=
ax
2
y
=
ax
2
+
k
y
=
a
(
x
-
h
)
2
y
=
a
(
x
-
h
)
2
+
k
y
=
ax
2
+
bx
+
c
瀵圭О杞?/p>
y
杞?/p>
y
杞?/p>
x
=
h
x
=
h
a
b
x
2
飥?
飥?/p>
椤剁偣
(0
锛?/p>
0)
(0
锛?/p>
k
)
(
h
锛?/p>
0)
(
h
锛?/p>
k
)
飪?/p>
飪?/p>
飪?
飪?/p>
飪?/p>
飪?/p>
飪?
飪?/p>
飥?/p>
飥?/p>
a
b
ac
a
b
4
4
,
2
2
a
>0
鏃讹紝椤剁偣鏄渶浣庣偣锛屾鏃?/p>
y
鏈夋渶灏忓�硷紱
a
<0
鏃讹紝椤剁偣鏄渶楂樼偣锛屾鏃?/p>
y
鏈夋渶澶?
鍊笺�?/p>
鏈�灏忓�?/p>
(
鎴栨渶澶у�?/p>
)
涓?/p>
0
(
k
鎴?/p>
a
b
ac
4
4
2
飥?/p>
)
銆?/p>
澧?/p>
鍑?/p>
鎬?/p>
a
>0
x
<0
(
h
鎴?/p>
a
b
2
飥?
)
鏃讹紝
y
闅?/p>
x
鐨勫澶ц�屽噺灏忥紱
x
>0
(
h
鎴?/p>
a
b
2
飥?/p>
)
鏃讹紝
y
闅?/p>
x
鐨勫澶ц�屽澶с�?/p>
鍗冲湪瀵圭О杞寸殑宸﹁竟锛?/p>
y
闅?/p>
x
鐨勫澶ц�屽噺灏忥紱鍦ㄥ绉拌酱鐨勫彸杈癸紝
y
闅?/p>
x
鐨勫澶ц�屽澶с�?/p>
a
<0
x
<0
(
h
鎴?/p>
a
b
2
飥?
)
鏃讹紝
y
闅?/p>
x
鐨勫澶ц�屽澶э紱
x
>0
(
h
鎴?/p>
a
b
2
飥?/p>
)
鏃讹紝
y
闅?/p>
x
鐨勫澶ц�屽噺灏忋�?/p>
鍗冲湪瀵圭О杞寸殑宸﹁竟锛?/p>
y
闅?/p>
x
鐨勫澶ц�屽澶э紱鍦ㄥ绉拌酱鐨勫彸杈癸紝
y
闅?/p>
x
鐨勫澶ц�屽噺灏忋�?/p>
3
銆佷簩娆″嚱鏁?/p>
y
=
ax
2
+
bx
+
c
涓庝竴鍏冧簩娆℃柟绋?/p>
ax
2
+
bx
+
c
=0
鐨勮仈绯伙細
(1)
濡傛灉鎶涚墿绾?/p>
y
=
ax
2
+
bx
+
c
涓?/p>
x
杞存湁鍏叡鐐癸紝鍏叡鐐圭殑妯潗鏍囨槸
x
0
锛岄偅涔堝綋
x
=
x
0
鏃讹紝鍑?/p>
鏁板�兼槸
0
锛屽洜姝?/p>
x
=
x
0
鏄柟绋?/p>
ax
2
+
bx
+
c
=0
鐨勪竴涓牴锛?/p>
(2)
鎶涚墿绾夸笌
x
杞寸殑浜ょ偣鍜屼竴鍏冧簩娆℃柟绋嬬殑鏍圭殑鍏崇郴
鎶涚墿绾?/p>
y
=
ax
2
+
bx
+
c
涓?/p>
x
杞寸殑浣嶇疆
涓�鍏冧簩娆℃柟绋?/p>
ax
2
+
bx
+
c
=0
鐨勮В
b
2
-
4
ac
>0
涓や釜鍏叡鐐?/p>
涓や釜涓嶇浉绛夌殑瀹炴暟鏍?/p>
b
2
-
4
ac
=0
涓�涓叕鍏辩偣
涓や釜鐩哥瓑鐨勫疄鏁版牴
b
2
-
4
ac<
0
娌℃湁鍏叡鐐?/p>
娌℃湁瀹炴暟鏍?/p>
1
銆侀�氳繃瀵瑰疄闄呴棶棰樼殑鍒嗘瀽锛屼綋浼氫簩娆″嚱鏁扮殑鎰忎箟銆?/p>
2
銆佷細鐢ㄦ弿鐐规硶鐢诲嚭浜屾鍑芥暟鐨勫浘璞★紝閫氳繃鍥捐薄浜嗚В浜屾鍑芥暟鐨勬�ц川銆?/p>
3
銆?/p>
浼氱敤閰嶆柟娉曞皢鏁板瓧绯绘暟鐨勪簩娆″嚱鏁扮殑琛ㄨ揪寮忓寲涓?/p>
y
=
a
(
x
-
h
)
2
+
k
鐨勫舰寮忥紝
骞惰兘鐢辨寰楀埌
鐭ヨ瘑瑕佺偣
璇炬爣瑕佹眰